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  <title>Testing MathJax v3 with TeX input and SVG output</title>
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    <h1>MathJax v3 beta: TeX input, SVG output test</h1>

    <p>
    When $a \ne 0$, there are two solutions to \(ax^2 + bx + c = 0\) and they are
    $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$
    </p>

    <h2>The Lorenz Equations</h2>

    <p>
    \begin{align}
    \dot{x} &amp; = \sigma(y-x) \\
    \dot{y} &amp; = \rho x - y - xz \\
    \dot{z} &amp; = -\beta z + xy
    \end{align}
    </p>

    <h2>The Cauchy-Schwarz Inequality</h2>

    <p>\[
    \left( \sum_{k=1}^n a_k b_k \right)^{\!\!2} \leq
     \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
    \]</p>

    <h2>A Cross Product Formula</h2>

    <p>\[
      \mathbf{V}_1 \times \mathbf{V}_2 =
       \begin{vmatrix}
        \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
        \frac{\partial X}{\partial u} &amp; \frac{\partial Y}{\partial u} &amp; 0 \\
        \frac{\partial X}{\partial v} &amp; \frac{\partial Y}{\partial v} &amp; 0 \\
       \end{vmatrix}
    \]</p>

    <h2>The probability of getting \(k\) heads when flipping \(n\) coins is:</h2>

    <p>\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]</p>

    <h2>An Identity of Ramanujan</h2>

    <p>\[
       \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} =
         1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
          {1+\frac{e^{-8\pi}} {1+\ldots} } } }
    \]</p>

    <h2>A Rogers-Ramanujan Identity</h2>

    <p>\[
      1 +  \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
        \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
         \quad\quad \text{for $|q| &lt; 1$}.
    \]</p>

    <h2>Maxwell's Equations</h2>

    <p>
    \begin{align}
      \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\
      \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
      \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
      \nabla \cdot \vec{\mathbf{B}} &amp; = 0
    \end{align}
    </p>

    <h2>In-line Mathematics</h2>

    <p>Finally, while display equations look good for a page of samples, the
    ability to mix math and text in a paragraph is also important.  This
    expression \(\sqrt{3x-1}+(1+x)^2\) is an example of an inline equation.  As
    you see, MathJax equations can be used this way as well, without unduly
    disturbing the spacing between lines.</p>
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